Question

complete the following truth table. use t for true and f for false.
you may add more columns, but those added columns will not be graded.

p q ~(q ∧ ~p)
t t
t f
f t
f f

not graded

Explanation:

Step1: Calculate $\sim p$

For $p=T$, $\sim p=F$; for $p=F$, $\sim p=T$

Step2: Calculate $q \land \sim p$

• $p=T,q=T$: $T \land F = F$
• $p=T,q=F$: $F \land F = F$
• $p=F,q=T$: $T \land T = T$
• $p=F,q=F$: $F \land T = F$

Step3: Negate the result of Step2

• For $F$: $\sim F = T$
• For $T$: $\sim T = F$

Answer:

$p$	$q$	$\sim p$	$\sim (q \land \sim p)$
T	F	F	T
F	T	T	F
F	F	T	T